Application of the Simultaneous Perturbation Stochastic Approximation Algorithm for Process Optimization: Case Study

Application of the Simultaneous Perturbation Stochastic Approximation Algorithm for Process Optimization: Case Study

Juan Carlos Castillo Garcia (Universidad Autónoma de Baja California, Mexico), Jesús Everardo Olguín Tiznado (Universidad Autónoma de Baja California, Mexico), Claudia Camargo Wilson (Universidad Autónoma de Baja California, Mexico), Juan Andrés López Barreras (Universidad Autónoma de Baja Calirfonia, Mexico) and Rafael García Martínez (Instituto Tecnológico de Guaymas, Mexico)
DOI: 10.4018/978-1-7998-1518-1.ch014

Abstract

There are different techniques for the optimization of industrial processes that are widely used in industry, such as experimental design or surface response methodology to name a few. There are also alternative techniques for optimization, like the Simultaneous Perturbation Stochastic Approaches (SPSA) algorithm. This chapter compares the results that can be obtained with classical techniques against the results that alternative linear search techniques such as the Simultaneous Perturbation Stochastic Approaches (SPSA) algorithm can achieve. Authors start from the work reported by Gedi et al. 2015 to implement the SPSA algorithm. The experiments allow authors to affirm that for this case study, the SPSA is capable of equalizing, even improving the results reported by the authors.
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Background

When you are trying to improve a process, there are two basic ways to obtain the necessary information: one is to observe or monitor using statistical tools, until you obtain useful signals that allow you to improve it; it is said that this is a passive strategy. The other way is to experiment, making strategic and deliberate changes to the process to provoke these useful signals. Design of experiments (DOE) is a set of active techniques, in the sense that they do not expect the process to send useful signals, but rather that it is “manipulated” to provide the information required for its improvement (Pulido, H. G. et al., 2012) .

The design of experiments is the application of the scientific method to generate knowledge about a system or process, by means of properly planned tests. This methodology has been consolidated as a set of statistical and engineering techniques that allows a better understanding of complex cause-effect situations (Montgomery, 2017).

The objective of a factorial design is to study the effect of different factors on one or several responses, when the same interest is had on all factors (Lujan-Moreno et al., 2018). For example, one of the most important objectives of a factorial design is to determine the combination of levels of controllable factors that will improve process performance.

The factors can be qualitative or quantitative. In order to study the influence of each factor on the response variable, it is necessary to choose at least two test levels for each of them. With a full factorial design, all possible combinations between the levels of the factors to be tested are studied.

However, there are many experimental designs to study the different types of industrial processes. And it is necessary to know how to choose among these types of designs the one that is most appropriate for each situation (Lauro, C. H. et al., 2016) . There are five aspects that influence the selection of an experimental design, in the meaning that when these aspects change, they usually lead us to change the design;

  • 1.

    The objective of the experiment,

  • 2.

    The number of factors to be studied,

  • 3.

    The number of levels tested on each factor,

  • 4.

    The affects you are interested in investigating,

  • 5.

    The cost of the experiment, the time and the desired precision.

According to their objective, experimental designs can be classified as follows (Pulido & Salazar, 2012):

  • Designs to compare two or more treatments

    • o

      Completely random designs (Montgomery, 2017)

    • o

      Random complete block designs, (Cheng, 2016)

    • o

      Latin Squares designs (Anderson, M. J., & Whitcomb, 2016)

    • o

      Greco-Latin square designs (Montgomery, 2017), (MacCalman, et al., 2017)

  • Designs to study the effect of several factors on one or more response variables

    • o

      2n factorial designs, (Kleijnen, 2015)

    • o

      3n factorial designs, (Malik & Pakzad, 2018)

    • o

      2n-p fractional factorial designs (Douaik, 2016)

  • Designs for process optimization, these can be divided into designs for

    • o

      First-order models

      • 2n factorial designs, (Kleijnen, 2015)

      • 2n-p fractional factorial designs, (Douaik, 2016), (Kleijnen, 2005)

      • Plackett burman design, (Douaik, 2016), (Kleijnen, 2005)

      • Simplex Design (Briones, F. Z. et al., 2016),

    • o

      and designs for second-order models

      • Central composite design, (Malik & Pakzad, 2018), (Salvatori, P. E. et al., 2018), (Douaik, 2016).

      • Box-Behnken design, (Malik & Pakzad, 2018), (Douaik, 2016)

      • 3n factorial designs, (Malik & Pakzad, 2018)

      • 3n-p fractional factorial designs (Montgomery, 2017)

  • Robust designs

    • o

      Orthogonal Array Designs(Cheng, 2016), (Dersjö, T., & Olsson, 2012)

    • o

      Design with internal and external arrangement (Heise, S. et al., 2018), (Briones, F. Z. et al., 2016)

  • Mixture design

    • o

      Axial design (Salvatori, P. E. et al.,2018)

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